Krishna is the incarnation of the Supreme Godhead. Hinduism believes that God descends on this earth time and again to restore Dharma, protect the noble and pious, and destroy the wicked and evil ones. The term Mukund is one of the most popular names of Lord Vishnu and hence Krishna is addressed with this name.
Splitting it into its syllables, the Sanskrit term Mukund can be interpreted as (Mu – liberation or Mukti; Ku – material existence; da – one who bestows) the supreme Godhead who can redeem us from the material existence and confer Mukti or liberation.
In a reference to Bhagavad Gita, Bhagavan Sri Sathya Sai Baba says in His book Geetha Vahini, “For the Geetha is the “milk” of the Upanishads, “drawn” by the Cowherd Krishna with the help of Arjuna, “the calf,” for all the “dull-witted” to drink and draw sustenance from.”
The primary task of any Avatar (divine incarnation) is to teach the mankind the highest wisdom. Avatars descend on this earth so that the humans can ascend to the higher consciousness and the supreme state of existence.
Here, it is very appropriate to make a reference to two verses from the Bhagavad Gita.
Sarva Dharmaan Parithyajya Maam Ekam Sharanam Vraja
Aham Tvaa Sarva Paapebhyo Moksha Ikshyaami Maa Shucha
Ye Man! Leave all the different ways prescribed by the texts. Take refuge in Me alone. I will wash out all your sins and confer the highest state of Mukti or liberation.
Ananyas Chintayantomaa Ye Jana Paryupaasate
Teshaam Nityaabhi Yuktaanaam Yoga Kshemam Vahaam Yaham
If one worships me constantly without any other thought, I shall take care of their material as well as spiritual well-being.
Therefore, Krishna is Mukund since his divine mission on the earth is to liberate people from the cycles of birth and death (due to ignorance and attachment) and confer the highest state of liberation or Mukti.